Spread spectrum signals are used in digital radio systems for telecommunication and navigation purposes. In particular, in a Global Positioning System (GPS), which is a well known spread spectrum system, a receiver processes several spread spectrum signals, each one emitted by a different satellite, to track the distance of the receiver from each satellite and, thereby, to determine its own position. In telecommunication systems, spread spectrum signals are used for (i) combatting interference, (ii) transmitting at very low power to avoid detection/interception, and (iii) multiplexing one channel over many users.
The basic operations of spread spectrum processing are (a) signal spreading, that is, bandwidth expansion of the transmitted signal by a large factor (typically higher than 100) through pseudorandom noise modulation, and (b) signal despreading, that is, bandwidth compression of the received signal by the same factor, which is often referred to as the "processing gain". These operations spread the power of any incident interference over the whole system bandwidth, so that, after signal despreading, the effective interference power is suppressed by a factor equal to the processing gain. Bandwidth expansion in spread spectrum systems is implemented by two methods. In direct sequence/spread spectrum (DS/SS) systems, for example, each data bit is mapped into a pseudorandom noise (PN) sequence of binary pulses (chip pulses). In frequency hopped/spread spectrum (FH/SS) systems, each data bit, or data bit fraction, is modulated by a different carrier so that the record of used carrier frequencies constitutes a PN sequence. In both methods, signal despreading is accomplished by correlating the received signal with the known PN chip or carrier frequency sequence.
In a DS/SS receiver it is possible to suppress a narrowband interferer beyond the processing gain, by filtering the received signal prior to despreading through an adaptive transversal filter (ATF). An ATF estimates the interference component in a reference input sample X.sub.i through an optimal linear combination X.sub.i =W.sub.N X.sub.i-N +. . . +W.sub.1 X.sub.i-1 +W.sub.-1 X.sub.i+1 +. . . +W.sub.-.sub.M X.sub.i+M of N past samples X.sub.i-1 . . . , X.sub.i-N and M future samples X.sub.i+1, . . . , X.sub.i+M, which are typically spaced one-chip interval apart. Interference is suppressed by subtracting the estimate X.sub.i from the reference X.sub.i and the difference Y.sub.i is the ATF output, i.e., Y.sub.i =X.sub.i -X.sub.i. If the interference is estimated from past samples only (i.e., as in prediction filtering), the ATF is referred to as a one-sided ATF. If future samples, as well as past samples, are used (i.e., as in interpolation filtering) then the ATF is referred to as a two-sided ATF.
Besides suppressing interference, the above filtering increases the thermal noise and distorts the PN-code in ATF output Y. The excess thermal noise is due to combining the thermal noise in X.sub.i together with N+M (statistically independent) noise components in the samples X.sub.i-k. The PN-code distortion is due to combining the PN-code in X.sub.i together with N+M versions of the PN-code which are time-shifted by k chips, k=-M to N, from the reference. PN-code distortion results in interchip interference in telecommunication systems, and in code-phase bias in navigation systems. The ATF gain corresponds to the net benefit of interference suppression minus the signal-to-noise (SNR) losses due to excess thermal noise and PN-code distortion. The ATF gain increases as the PN-code components of the combined samples become less correlated and the interference components become more correlated. Since the correlation between consecutive signal samples increases as the signal power spectrum gets narrower, significant ATF gain is expected when the interference spectrum occupies a small fraction, typically less than 10%, of the PN-code bandwidth (i.e., system bandwidth). In the frequency domain, the operation of ATF corresponds to discriminating against the interference spectrum by forming a linear filter (through the appropriate weights W.sub.k) with a notch around the center frequency of the interferer. Accordingly, ATF is not very effective against wideband interference, but it is very effective against continuous-wave (CW) interference and other narrowband interferences, such as pulsed CW and swept CW.
Assuming that the interference has an adequately narrowband spectrum for ATF application, there are two critical system requirements for achieving significant ATF gain. First, there must be adequate means for filtering and, secondly, there must be adequate means for generating automatically appropriate weights.
Regarding the filtering aspect thereof, the ATF must be capable of combining a minimum number of input samples to estimate the interference, which operation relates to the number of delay line taps used in the filter, each tap providing a signal to be weighted and added to the rest of the tap signals. If the interference forms K well-separated spectral bands, the minimum number of taps is 2K because the ATF needs to introduce at least one spectral notch at each interference band, at the expense of two taps (i.e., real weight coefficients) per notch. A disadvantage of increasing the number of taps is the resulting increase in system complexity. In this regard, a significant advantage of a symmetric two-sided ATF (in which M=N), compared to the one-sided ATF, is the symmetry of the optimal weights W.sub.i =W.sub.-i. Therefore, at least in steady-state, a 2N-tap ATF filter requires only N weight-updating circuits. It has been determined that for the same number of taps, a symmetric two-sided ATF yields the same gain as a one-sided ATF, but its optimal weights are much smaller (e.g., up to 50% smaller) resulting in decreased PN-code distortion. Therefore, the symmetric two-sided ATF is the preferred ATF architecture for DS/SS systems.
Regarding automatic weight generation, the optimal weights depend on the interference characteristics and on the criterion of optimality or cost function. An effective cost function for spread-spectrum systems subjected to strong interference is the average power of the ATF output signal Y. This is referred to as Mean Square Error (MSE) criterion, the error being equal to the ATF output. Classical MSE theory shows that the optimal weights can be obtained by solving a set of 2N linear equations (normal equations), which involve the correlation function of the ATF input signal. This is not a practical implementation approach due to the complexity of frequent updating of the input correlation estimates and solving the normal equations. Both of these complications can be avoided through an iterative solution of the normal equations. In this case, each weight is updated in every sampling interval, so that, after several updates, it tends to the MSE-optimal weight. A practical iterative algorithm, which has been shown to converge (on the average) to the optimal weights, is the Widrow-Hoff algorithm. This algorithm updates W.sub.k as: NEW(W.sub.k)=OLD(W.sub.k)+uX.sub.i-k Y.sub.i. The parameter u is referred to as the step-size (of the algorithm), and it controls the convergence characteristics and the steady-state weight jitter of the algorithm. As the step-size increases the adaptation converges faster, but the weights exhibit an increasing amount of jitter. If the step-size exceeds a certain threshold, depending on the largest eigenvalue of the normal equations, the weights grow in an erratic fashion, i.e., the algorithm does not converge. It has been determined, through ATF simulations in multiple CW interference, that the typical value of u =0.01 is a good compromise between convergence rate and steady-state jitter.
Although the theoretical principles of adaptive transversal filtering were introduced almost 30 years ago, it is desirable to develop better filtering techniques so as to reduce the cost and improve the performance thereof, as well as to expand the use thereof into many new applications. Currently available ATF implementations have principally been using analog devices such as Charge Couple Devices (CCD) and Surface Acoustic Wave (SAW) devices. The size, power, weight and cost of analog ATF implementation has often precluded its consideration for many practical applications.